1. Field of the Invention
The present invention relates to a method for demodulating and a demodulator for demodulating various signals by hard-decision techniques, such as phase shift keying (PSK) and quadrature amplitude modulation (QAM); as well as demodulating signals by soft-decision techniques, such as Viterbi decoding and trellis decoding. For hard-decision techniques, the decision regions are optimized at the receiver to reduce the bit error rate (BER); and for soft-decision techniques, the decision metrics are optimized at the receiver to reduce the bit error rate (BER). Optimizing the decision regions and metrics may obviate the need for non-linear predistortion at the transmitter.
2. Description of the Prior Art
Various modulation techniques are known for modulating a carrier signal with various types of information. Due to limited bandwidth allocations, modulation techniques have been developed to increase the amount of information that can be transmitted per frequency. One such technique is known as quadrature phase shift keying (QPSK). Such QPSK modulation techniques are known in the art and described in U.S. Pat. Nos. 5,440,259; 5,615,230; 5,440,268, 5,550,868; 5,598,441; 5,500,876 and 5,485,489, hereby incorporated by reference. In general, in such a modulation technique, the phase of both the real and quadrature components of the carrier are modulated to enable two bits, each having two stages, to be transmitted over a single frequency. As such, at each frequency, the carrier can be modulated into one of four different phase states, known as symbols, which form a constellation as generally shown in FIG. 1. The QPSK modulation technique is thus able to provide twice the information per frequency relative to amplitude and frequency modulation techniques, making it suitable for applications in which bandwidth allocations are relatively limited, for example, in satellite communications systems.
In order to further increase the amount of information transmitted per frequency, other modulation techniques have been developed, such as quadrature amplitude modulation (QAM). Such QAM modulation techniques are relatively well-known in the art. Examples of such QAM modulation techniques are disclosed in U.S. Pat. Nos. 5,612,651; 5,343,499; 5,363,408; and 5,307,377; hereby incorporated by reference. Such QAM modulation techniques essentially involve amplitude and phase modulation of a QPSK signal to provide constellations of signals of 8, 16, 32 and 64 and more, for example, as illustrated in FIG. 2.
Decoding of PSK and QAM modulated signals is also known in the art. In general, the PSK or QAM signal is received, demodulated, filtered and sampled. The sample is known as the decision variable. For example, the QPSK constellation illustrated in FIG. 1 can be divided into four symmetric decision regions, each representing one quadrant, identified with the reference numerals 20, 21, 22 and 26. Similarly, for an 8PSK constellation as illustrated in FIG. 3, there are 8 decision regions 30, 32, 34, 36, 38, 40, 42 and 44. Each decisions region 30–44 is defined by a rotationally symmetric 45° slice of a pie as shown by the dotted lines in FIG. 3. In order to decode the symbols, the bit or symbol decisions are based upon determining the decision region in which the decision variable is located. This technique is known as hard-decision detection.
Other coding and decoding techniques are known, such as trellis decoding and Viterbi decoding. Trellis coded demodulation is discussed in detail in U.S. Pat. No. 4,873,701, hereby incorporated by reference. Convolutional coding techniques are also known. Such convolutionally coded signals are known to be decoded by a procedure, known as Viterbi decoding. Viterbi decoding is discussed in “Error Bounds for Convolutional Codes and Asymptotically Optimum Decoding Algorithm” by A. J. Viterbi, IEEE Trans. Inf. Theory, IT-13 pp. 260–269, April 1967. Convolutional coding/Viterbi decoding techniques are also disclosed in “Error Coding Cookbook”, by C. Britton Rorabaugh, McGraw Hill copyright 1996, pp. 105–125, hereby incorporated by reference. Such techniques are known as soft-decision techniques. In such soft-decision techniques, a decision metric is typically computed as the distance between the received decision variable and a reference constellation.
Unfortunately, there are problems associated with the hard-decision techniques as well as the soft-decision techniques which lead to a degradation in the error rate (BER) performance of the system. Such problems are a result of modulator implementation imperfections, channel filtering, amplifier non-linearities and demodulator imperfections. These various problems result in the noise-free decision variables not being at their ideal locations and not equidistant from the nearest decision boundaries. As such, decisions that are made relative to the ideal decision regions are less than ideal leading to an increased BER. In soft-decision decoding techniques, the problems mentioned above result in the noise free constellation not being at an ideal location.
These problems are best understood with reference to FIGS. 4 and 5 which illustrate a binary phase shift keying (BPSK) example. As shown in FIG. 4, the constellation points ±A are equidistant from the zero axis which acts as a decision boundary. The additive white Gaussian noise (AWGN) probability density functions (PDF) are shown for the two constellation points ±A. As shown, the modulator output signals are transmitted with equal probability providing maximum likelihood decision-making which minimizes the BER.
A non-ideal condition is illustrated in FIG. 5. In this FIG. 5, the constellation points +B and −C have uncalibrated biases, for example, due to modem imperfections, amplifier non-linearity and the like. As shown, the constellation points +B and −C are no longer equidistant to the decision boundary. As such, the decision region boundary no longer provides the maximum likelihood of probability and the probability of error is significantly increased thereby increasing the BER. Thus, there is a need for providing an improved decoding technique which optimizes the BER.